Refraction of nonlinear light beams in nematic liquid crystals

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Abstract

Optical spatial solitons in nematic liquid crystals, termed nematicons, have become an excellent
test bed for nonlinear optics, ranging from fundamental effects to potential uses, such as designing
and demonstrating all-optical switching and routing circuits in reconfigurable settings
and guided-wave formats. Following their demonstration in planar voltage-assisted nematic
liquid crystal cells, the spatial routing of nematicons and associated waveguides have been successfully
pursued by exploiting birefringent walkoff, interactions between solitons, electro-optic
controlling, lensing effects, boundary effects, solitons in twisted arrangements, refraction and
total internal reflection and dark solitons. Refraction and total internal reflection, relying on
an interface between two dielectric regions in nematic liquid crystals, provides the most striking
results in terms of angular steering. In this thesis, the refraction and total internal reflection
of self-trapped optical beams in nematic liquid crystals in the case of a planar cell with two
separate regions defined by independently applied bias voltages have been investigated with the
aim of achieving a broader understanding of the nematicons and their control. The study of
the refraction of nematicons is then extended to the equivalent refraction of optical vortices.
The equations governing nonlinear optical beam propagation in nematic liquid crystals are
a system consisting of a nonlinear Schr¨odinger-type equation for the optical beam and an elliptic
Poisson equation for the medium response. This system of equations has no exact solitary
wave solution or any other exact solutions. Although numerical solutions of the governing
equations can be found, it has been found that modulation theories give insight into the mechanisms
behind nonlinear optical beam evolution, while giving approximate solutions in good
to excellent agreement with full numerical solutions and experimental results. The modulation
theory reduces the infinite-dimensional partial differential equation problem to a finite dynamical
system of comparatively simple ordinary differential equations which are, then easily solved
numerically. The modulation theory results on the refraction and total internal reflection of
nematicons are in excellent agreement with experimental data and numerical simulations, even
when accounting for the birefringent walkoff. The modulation theory also gives excellent results
for the refraction of optical vortices of +1 topological charge. The modulation theory
predicts that the vortices can become unstable on interaction with the nematic interface, which
is verified in quantitative detail by full numerical solutions. This prediction of their azimuthal
instability and their break-up into bright beams still awaits an experimental demonstration, but
the previously obtained agreement of modulation theory models with the behaviour of actual
nematicons leads us to expect the forthcoming observation of the predicted effects with vortices
as well.